What are the solutions to the equation x(x-3)=5x-7 ?

The solutions to the equation x(x-3)=5x-7 are x=7,x=1

Find the zeros of x(x-3)=5x-7

The zeros of x(x-3)=5x-7 are x=7,x=1

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x (x - 3) = 5 x - 7

x = 7, x = 1

Solution steps

x (x - 3) = 5 x - 7

Expand

x (x - 3) : x^{2} - 3 x

x^{2} - 3 x = 5 x - 7

Move

7

to the left side

x^{2} - 3 x + 7 = 5 x

Move

5 x

to the left side

x^{2} - 8 x + 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot 7}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot 7 = 6

x_{1, 2} = \frac{- ( - 8 ) \pm 6}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 6}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 6}{2 \cdot 1}

x = \frac{- ( - 8 ) + 6}{2 \cdot 1} : 7

x = \frac{- ( - 8 ) - 6}{2 \cdot 1} : 1

The solutions to the quadratic equation are:

x = 7, x = 1

x^{2} - 7 = x + 5

x^{2} - 7 x + 20 = 10

7 x^{2} + 25 x = 12

x^{2} - 3 x = 108

400 - 16 x^{2} = 0

What are the solutions to the equation x(x-3)=5x-7 ?
The solutions to the equation x(x-3)=5x-7 are x=7,x=1
Find the zeros of x(x-3)=5x-7
The zeros of x(x-3)=5x-7 are x=7,x=1